Single machine SLK/DIF due window assignment problem with job-dependent linear deterioration effects

We consider single machine scheduling problems with deteriorating jobs and SLK/DIF due window assignment, where the deteriorating rates of jobs are assumed to be job‐dependent. We consider two different objectives under SLK and DIF due window assignment, respectively. The first objective is to minimise total costs of earliness, tardiness, due window location and due window size, while the second objective is to minimise a cost function that includes number of early jobs, number of tardy jobs and the costs for due window location and due window size. We study the optimality properties for all problems and develop algorithms for solving these problems in polynomial time.